Question

Question content area top
Part 1
The area of a square frame is 55 square inches. Find the length of one side of the frame. Explain.
a. to the nearest whole inch
b. to the nearest tenth of an inch
Question content area bottom
Part 1
a. The length of one side of the frame to the nearest whole inch is
  
enter your response here in.
Part 2
Explain.
  
enter your response hereless than55less than
  
enter your response here​, so
  
enter your response hereless thanStartRoot 55 EndRootless than
  
enter your response here. Since 55 is closer to
  
enter your response here than to
  
enter your response here​, StartRoot 55 EndRoot is closer to
  
enter your response here.
​(Type integers or​ decimals.)
Part 3
b. The length of one side of the frame to the nearest tenth of an inch is
  
enter your response here in.
Part 4
Explain.
▼
7.2 times 7.2
7.6 times 7.6
7.8 times 7.8
7.4 times 7.4
equals
  
enter your response here and
▼
7.3 times 7.3
7.1 times 7.1
7.5 times 7.5
7.7 times 7.7
equals
  
enter your response here. Since 55 is closer to
  
enter your response here than to
  
enter your response here​,
  
enter your response here is a better approximation of the side length.
​(Type integers or​ decimals.)

Answer 1

a. 7 in.

Explain:
49 < 55 < 64, so 7 < √55 < 8. Since 55 is closer to 49 than to 64, √55 is closer to 7 than to 8.

b. 7.4 in.

Explain:
7.4 × 7.4 = 54.76 and 7.5 × 7.5 = 56.25. Since 55 is closer to 54.76 than to 56.25, 7.4 is a better tenth‑place approximation (√55 ≈ 7.416).